Electrical analogous in viscoelasticity

Abstract

a b s t r a c tIn this paper, electrical analogous models of fractional hereditary materials are introduced. Based on recent works by the authors, mechanical models of materials viscoelasticity behavior are firstly approached by using fractional mathematical operators. Viscoelastic models have elastic and viscous components which are obtained by combining springs and dashpots. Various arrangements of these elements can be used, and all of these viscoelastic models can be equivalently modeled as electrical circuits, where the spring and dashpot are analogous to the capacitance and resistance, respectively. The proposed models are validated by using modal analysis. Moreover, a comparison with numerical experiments based on finite difference time domain method shows that, for long time simulations, the correct time behavior can be obtained only with modal analysis. The use of electrical analogous in viscoelasticity can better reveal the real behavior of fractional hereditary materials.

Electrical analogs for Kelvin & Maxwell viscoelastic materials: Applications to cornea & sclera

“…In addition, the material properties of the track surface, i.e. Tartan, polyurethane, Astroturf, Tuned Track, macadam, cinders, natural grass, plywood, fiberglass, etc., are modeled as a viscoelastic material [19][20][21].…”

“…The more complicated 4-element Windkessel model includes the inertial effects of the circulatory system, modeled with an inductor. These techniques are particularly useful in terms of calculating cardio-vascular pulse-wave reflections, modeling the circulatory system as a transmission line, using Smith-chart techniques [16][17][18][19][20][21][22][23][24][25][26].…”

Viscoelasticity: An electrical point of view

“…VE material can be viewed by an indefinite shear type column resting on a bed of independent dashpots [8]. Discrete models of these continuous behaviors are depicted [9] and then, a general electrical analogous circuit is introduced in order to predict the behavior of FHM in an alternative way [13]. The proposed analogies are validated by using modal analysis.…”

“…For an intermediate electrical behavior, between the purely capacitive and the purely resistive, a fractional current-voltage relation results. So a proper fractional electrical model of viscoelasticity can be straightforwardly obtained [13].…”

“…5 can be obtained by considering the C-R cell valid for a small but finite abscissa intervals ∆x [13]. By introducing a discretization of the x-axis as x j = j∆x into the governing Eq.…”